(Solution) - If a matrix is sensitive to roundoff errors the computed -(2025 Original AI-Free Solution)

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If a matrix is sensitive to roundoff errors, the computed value of its determinant may differ drastically from the exact value. For an example of this, set
U = round(l00 * rand(l0)); U = triu((U, 1) + 0.1 * eye(10)
In theory,
det(U) = det(UT) = 10-10
and
det(UUT) = det(U) det(UT) = 10-20
Compute det(U), det(U?), and det(U * U?) using MATLAB. Do the computed values match the theoretical values?